static const float lut[256] = {
    0,
    0.000303526983548838,
    0.000607053967097675,
    0.000910580950646513,
    0.00121410793419535,
    0.00151763491774419,
    0.00182116190129303,
    0.00212468888484186,
    0.0024282158683907,
    0.00273174285193954,
    0.00303526983548838,
    0.00334653576389916,
    0.00367650732404744,
    0.00402471701849631,
    0.00439144203741029,
    0.00477695348069373,
    0.00518151670233839,
    0.00560539162420272,
    0.00604883302285705,
    0.00651209079259448,
    0.00699541018726539,
    0.00749903204322618,
    0.00802319298538499,
    0.00856812561806931,
    0.00913405870222079,
    0.00972121732023785,
    0.0103298230296269,
    0.0109600940064882,
    0.0116122451797439,
    0.0122864883569159,
    0.012983032342173,
    0.0137020830472897,
    0.0144438435960925,
    0.0152085144229127,
    0.0159962933655096,
    0.0168073757528874,
    0.0176419544883841,
    0.0185002201283797,
    0.0193823609569357,
    0.0202885630566524,
    0.0212190103760036,
    0.0221738847933874,
    0.0231533661781104,
    0.0241576324485048,
    0.0251868596273616,
    0.0262412218948499,
    0.0273208916390749,
    0.0284260395044208,
    0.0295568344378088,
    0.0307134437329936,
    0.0318960330730115,
    0.0331047665708851,
    0.0343398068086822,
    0.0356013148750203,
    0.0368894504011,
    0.0382043715953465,
    0.0395462352767328,
    0.0409151969068532,
    0.0423114106208097,
    0.0437350292569735,
    0.0451862043856755,
    0.0466650863368801,
    0.0481718242268894,
    0.0497065659841272,
    0.0512694583740432,
    0.0528606470231802,
    0.0544802764424424,
    0.0561284900496001,
    0.0578054301910672,
    0.0595112381629812,
    0.0612460542316176,
    0.0630100176531677,
    0.0648032666929058,
    0.0666259386437729,
    0.0684781698444002,
    0.0703600956965959,
    0.0722718506823175,
    0.0742135683801496,
    0.0761853814813079,
    0.0781874218051863,
    0.0802198203144683,
    0.0822827071298148,
    0.0843762115441488,
    0.0865004620365498,
    0.0886555862857729,
    0.0908417111834077,
    0.0930589628466875,
    0.0953074666309647,
    0.0975873471418625,
    0.0998987282471139,
    0.102241733088101,
    0.104616484091104,
    0.107023102978268,
    0.109461710778299,
    0.111932427836906,
    0.114435373826974,
    0.116970667758511,
    0.119538427988346,
    0.122138772229602,
    0.12477181756095,
    0.127437680435647,
    0.130136476690364,
    0.132868321553818,
    0.135633329655206,
    0.138431615032452,
    0.141263291140272,
    0.144128470858058,
    0.147027266497595,
    0.149959789810609,
    0.15292615199615,
    0.155926463707827,
    0.15896083506088,
    0.162029375639111,
    0.165132194501668,
    0.168269400189691,
    0.171441100732823,
    0.174647403655585,
    0.177888415983629,
    0.18116424424986,
    0.184474994500441,
    0.187820772300678,
    0.191201682740791,
    0.194617830441576,
    0.198069319559949,
    0.201556253794397,
    0.205078736390317,
    0.208636870145256,
    0.212230757414055,
    0.215860500113899,
    0.219526199729269,
    0.223227957316809,
    0.226965873510098,
    0.230740048524349,
    0.234550582161005,
    0.238397573812271,
    0.242281122465555,
    0.246201326707835,
    0.250158284729953,
    0.254152094330827,
    0.258182852921596,
    0.262250657529696,
    0.266355604802862,
    0.270497791013066,
    0.274677312060385,
    0.27889426347681,
    0.283148740429992,
    0.287440837726918,
    0.291770649817536,
    0.296138270798321,
    0.300543794415777,
    0.304987314069886,
    0.309468922817509,
    0.313988713375718,
    0.318546778125092,
    0.323143209112951,
    0.327778098056542,
    0.332451536346179,
    0.33716361504833,
    0.341914424908661,
    0.34670405635503,
    0.351532599500439,
    0.356400144145944,
    0.36130677978351,
    0.36625259559884,
    0.371237680474149,
    0.376262122990907,
    0.38132601143253,
    0.386429433787049,
    0.391572477749723,
    0.396755230725627,
    0.401977779832196,
    0.407240211901737,
    0.412542613483904,
    0.417885070848138,
    0.423267669986072,
    0.428690496613907,
    0.434153636174749,
    0.439657173840919,
    0.445201194516228,
    0.450785782838223,
    0.456411023180405,
    0.462076999654407,
    0.467783796112159,
    0.47353149614801,
    0.479320183100827,
    0.48514994005607,
    0.491020849847836,
    0.49693299506087,
    0.502886458032569,
    0.508881320854934,
    0.514917665376521,
    0.520995573204354,
    0.527115125705813,
    0.533276404010505,
    0.539479489012107,
    0.545724461370187,
    0.552011401512,
    0.558340389634268,
    0.564711505704929,
    0.571124829464873,
    0.577580440429651,
    0.584078417891164,
    0.590618840919337,
    0.597201788363763,
    0.603827338855338,
    0.610495570807865,
    0.617206562419651,
    0.623960391675076,
    0.630757136346147,
    0.637596873994033,
    0.644479681970582,
    0.651405637419824,
    0.658374817279449,
    0.665387298282272,
    0.672443156957688,
    0.679542469633094,
    0.686685312435314,
    0.69387176129199,
    0.701101891932973,
    0.708375779891687,
    0.715693500506481,
    0.723055128921969,
    0.730460740090354,
    0.737910408772731,
    0.745404209540387,
    0.752942216776078,
    0.760524504675292,
    0.768151147247507,
    0.775822218317424,
    0.783537791526194,
    0.79129794033263,
    0.799102738014409,
    0.806952257669252,
    0.814846572216101,
    0.822785754396284,
    0.830769876774655,
    0.83879901174074,
    0.846873231509858,
    0.854992608124234,
    0.863157213454102,
    0.871367119198797,
    0.879622396887832,
    0.887923117881966,
    0.896269353374266,
    0.90466117439115,
    0.913098651793419,
    0.921581856277295,
    0.930110858375424,
    0.938685728457888,
    0.9473065367332,
    0.955973353249286,
    0.964686247894465,
    0.973445290398413,
    0.982250550333117,
    0.99110209711383,
    1,
};